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Methods in Dynamical Systems, Mathematics of Networks, and Optimization for Modelling in Engineering

A special issue of Applied Sciences (ISSN 2076-3417).

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 7101

Special Issue Editor

Dr. Ioannis Dassios

E-Mail Website
Guest Editor
School of Electrical and Electronic Engineering, University College Dublin, D04 V1W8 Dublin, Ireland
Interests: differential/difference equations; dynamical systems; modeling and stability analysis of electric power systems; mathematics of networks; fractional calculus; mathematical modeling (power systems, materials science, energy, macroeconomics, social media, etc.); optimization for the analysis of large-scale data sets; fluid mechanics; discrete calculus; Bayes control; e-learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue aims to gather the latest results related to dynamical systems, mathematics of networks, optimization, and their application in the mathematical modeling of engineering problems, such as concerning electrical power systems, materials, energy, any many more.

This Special Issue will accept high-quality papers describing original research results with the purpose of bringing together mathematicians with engineers, as well as other scientists.

The following non-exhaustive list of topics will be covered:

  • Differential/difference equations
  • Partial differential equations
  • Dynamical systems
  • Mathematics of networks
  • Fractional calculus
  • Modeling and stability analysis of power systems
  • Discrete calculus
  • Circuits theory
  • Signal processing
  • Materials science
  • Energy systems

Dr. Ioannis Dassios
Guest Editor

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Published Papers (3 papers)

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Research

11 pages, 2993 KiB  
Article
On the Derivation of Multisymplectic Variational Integrators for Hyperbolic PDEs Using Exponential Functions
by Odysseas Kosmas, Pieter Boom and Andrey P. Jivkov
Appl. Sci. 2021, 11(17), 7837; https://doi.org/10.3390/app11177837 - 25 Aug 2021
Viewed by 1706
Abstract
We investigated the derivation of numerical methods for solving partial differential equations, focusing on those that preserve physical properties of Hamiltonian systems. The formulation of these properties via symplectic forms gives rise to multisymplectic variational schemes. By using analogy with the smooth case, [...] Read more.
We investigated the derivation of numerical methods for solving partial differential equations, focusing on those that preserve physical properties of Hamiltonian systems. The formulation of these properties via symplectic forms gives rise to multisymplectic variational schemes. By using analogy with the smooth case, we defined a discrete Lagrangian density through the use of exponential functions, and derived its Hamiltonian by Legendre transform. This led to a discrete Hamiltonian system, the symplectic forms of which obey the conservation laws. The integration schemes derived in this work were tested on hyperbolic-type PDEs, such as the linear wave equations and the non-linear seismic wave equations, and were assessed for their accuracy and the effectiveness by comparing them with those of standard multisymplectic ones. Our error analysis and the convergence plots show significant improvements over the standard schemes. Full article
(This article belongs to the Special Issue Methods in Dynamical Systems, Mathematics of Networks, and Optimization for Modelling in Engineering)
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11 pages, 289 KiB  
Article
Criteria for the Nonexistence of Kneser Solutions of DDEs and Their Applications in Oscillation Theory
by Osama Moaaz, Ioannis Dassios, Haifa Bin Jebreen and Ali Muhib
Appl. Sci. 2021, 11(1), 425; https://doi.org/10.3390/app11010425 - 4 Jan 2021
Cited by 8 | Viewed by 2111
Abstract
The objective of this study was to improve existing oscillation criteria for delay differential equations (DDEs) of the fourth order by establishing new criteria for the nonexistence of so-called Kneser solutions. The new criteria are characterized by taking into account the effect of [...] Read more.
The objective of this study was to improve existing oscillation criteria for delay differential equations (DDEs) of the fourth order by establishing new criteria for the nonexistence of so-called Kneser solutions. The new criteria are characterized by taking into account the effect of delay argument. All previous relevant results have neglected the effect of the delay argument, so our results substantially improve the well-known results reported in the literature. The effectiveness of our new criteria is illustrated via an example. Full article
(This article belongs to the Special Issue Methods in Dynamical Systems, Mathematics of Networks, and Optimization for Modelling in Engineering)
10 pages, 284 KiB  
Article
Oscillatory Properties of Odd-Order Delay Differential Equations with Distribution Deviating Arguments
by Ali Muhib, Thabet Abdeljawad, Osama Moaaz and Elmetwally M. Elabbasy
Appl. Sci. 2020, 10(17), 5952; https://doi.org/10.3390/app10175952 - 27 Aug 2020
Cited by 18 | Viewed by 1903
Abstract
Throughout this work, new criteria for the asymptotic behavior and oscillation of a class of odd-order delay differential equations with distributed deviating arguments are established. Our method is essentially based on establishing sharper estimates for positive solutions of the studied equation, using an [...] Read more.
Throughout this work, new criteria for the asymptotic behavior and oscillation of a class of odd-order delay differential equations with distributed deviating arguments are established. Our method is essentially based on establishing sharper estimates for positive solutions of the studied equation, using an iterative technique. Moreover, the iterative technique allows us to test the oscillation, even when the related results fail to apply. By establishing new comparison theorems that compare the nth-order equations with one or a couple of first-order delay differential equations, we obtain new conditions for oscillation of all solutions of the studied equation. To show the importance of our results, we provide two examples. Full article
(This article belongs to the Special Issue Methods in Dynamical Systems, Mathematics of Networks, and Optimization for Modelling in Engineering)
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